This question about Hero's Engine pop up regularly. I posted an answer here a while back. Perhaps it existed as something small, like a toy, but they never could have built one that could actually do work- or build the boiler to power it.

The notion has obvious appeal- it would be very satisfying if they didn't want to progress with good technology because they had slaves and so we could dislike them more for having them. Most people I think now get it from reading Zinn's A People's History ( a book that likes to jump to attractive conclusions) but it seems to have been around much longer. There were plenty of other factors getting in the way of an industrial revolution in the classical world ( like, the difficulty of capital formation without much of a legal framework for protecting investment). And there have been examples of slave-owning societies getting along fine with technology when it was useful- like all those plantations in the southern US pre-1865 using cotton gins to clean their cotton and steamboats to ship it.

However, technological advances do tend to follow the interests of the powerful. Labor-saving clothes-washers and dishwashers were certainly possible long before they became common household appliances , and it's notable that the first clothes-washers were invented and used by the Shakers- who gave women an equal role in their communes. And the first dishwasher was invented by a woman.

On top of what /u/Bodark43 has said, I'd offer this thread as well. It's the same user, but it's in rather more detail and I jumped in to sum up the historiography on the problem of the lack of a Roman industrial revolution. The idea that slavery somehow affected the need for Roman mechanical industry, either positively or negatively (both have been proposed, which throws a bit of a wrench in the nice, neatness of the idea!), has a long pedigree, and despite surviving in the popular discourse was more or less abandoned decades ago as an untenable thesis.